How do you solve using the completing the square method 3x^2-4x-2=0?

1 Answer
Shwetank Mauria
Aug 6, 2016

x=(-2-sqrt10)/3 or x=(-2+sqrt10)/3

Explanation:

Let us divide each term of 3x^2-4x-2=0 by 3, we get

x^2-4/3x-2/3=0

Now recalling the identity (x-a)^2=x^2-2ax+a^2 and comparing it with x^2-4/3x, we need to add and subtract (4/(3xx2))^2 to complete square. Hence x^2-4/3x-2/3=0 is

hArrx^2-2xx4/6x+(4/6)^2-(4/6)^2-2/3=0 or

(x+4/6)^2-(2/3)^2-2/3=0 or

(x+2/3)^2-4/9-6/9=0 or

(x+2/3)^2-10/9=0 or

(x+2/3)^2-(sqrt10/3)^2=0 or

(x+2/3+sqrt10/3)(x+2/3-sqrt10/3)=0

Hence, x+2/3+sqrt10/3=0 or x+2/3-sqrt10/3=0

i.e. x=(-2-sqrt10)/3 or x=(-2+sqrt10)/3

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